The ad-free version's purchase, like any other app, is associated to the Play Store or App Store account you use.
For this reason, as long as you use the same store account on your device, you will be able to download this version as many times as you wish without having to pay for it again.
If you switch to a device with the same operating system, it will be possible to download the app again free of charge as long as you use the same store account. If, on the other hand, you change your store account or your new device uses a different operating system, you will have to pay for the application again.
We recommend you visit the articles: I bought the ad-free version, why do I still see ads? and Why am I being asked to pay if I already bought the version ad-free version?